# [EM] PJ

Arthur Wist arthur.wist at gmail.com
Wed Jun 26 22:04:08 PDT 2019

```Hi,

This kinda reminds me of the Bayesian Truth Serum:

https://wesselb.github.io/assets/talks/serum.pdf

https://www.dropbox.com/s/dl/k8rdnbql1t0byxy/serum.pdf

Kind regards,

Arthur

On Wed, 26 Jun 2019, 20:11 Forest Simmons, <fsimmons at pcc.edu> wrote:

> Here's the simplest version of PJ:
>
> Voters submit approval ballots with favorite identified, and with a number
> between zero and 100 percent as their estimate of what degree of consensus
> is reasonably possible, the consensus potential estimate (CPE)
>
> After the approvals have been tallied, a ballot is drawn at random.
>
> If the approval winner's approval percentage is greater than both the
> median of all the consensus potential estimates, as well as the CPE on the
> drawn ballot, then the approval winner is elected.
>
> Otherwise the ballot favorite is elected.
>
> On Sat, Jun 22, 2019 at 4:23 PM Forest Simmons <fsimmons at pcc.edu> wrote:
>
>> PJ stands for either Proportional Judgment (as opposed to Majority
>> Judgment) or Poetic Justice (see if you agree).
>>
>> Voters submit approval ballots along with a circled favorite and a number
>> R between zero and one that the voter of the ballot thinks is a good
>> approval score given the chances for consensus.
>>
>> Let P (between zero and one) be the average approval of the approval
>> winner.  Let Q (between zero and one) be the median of the submitted
>> numbers.
>>
>> A ballot B is drawn.  Let R be the reasonable number marked on the
>> ballot, and let F be the indicated favorite.
>>
>> If R>P, then elect the favorite or the approval winner with
>> probabilities  R and (1-R) respectively.
>>
>> [Note that if R=P=1, the favorite must be the same as the approval
>> winner.]
>>
>> Otherwise (If R is no greater than P) ...
>> ... If P is in the closed interval [Q, 1], then elect the approval winner
>> .... else defer the decision to a second randomly drawn ballot.
>>
>> I admit there is room for tweaking, but my main idea is to give incentive
>> for the max possible consensus.
>>
>> The interesting case is when R is less than both P and Q.  In this case
>> both according to the voter of the random ballot and the median estimate of
>> reasonable possible consensus, the approval has fallen short of its
>> potential, so random favorite, the fall back benchmark, should be invoked.
>> Hence the second random ballot in this case.
>>
>> Does the whole process start over again with the second randomly drawn
>> ballot?  Possibly, but let's keep it simple.  Just take the favorite of the
>> second ballot.
>>
>> Why not just use F from the first random ballot in this case, with
>> probabilitty R, and revert to a second random ballot with probability
>> (1-R).  That is another possibility.  And I'm sure there are other
>> acceptable or even better ways to use the values of R, P, Q, and F to
>> decide what to do.
>>
>> I appreciate your thoughts.
>>
>> Forest
>>
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